How much material will be left if a radioactive isotope has a half life of 1.3 billion years in 3.9 billion years?

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Answer 1 · 2014-07-21T18:47:39

You will have 12.5 % of the parent material after 1.3 billion years.

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Method 1

In your problem, the number of half-lives is

$n$ $n$ = 3.9 billion years × $\frac{1 half-life}{1.3 billion years}$ $(1"half-life")/(1.3"billion years")$ = 3.0 half-lives

The amount remaining after 3 half-lives is

100 % × $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{100 %}{8}$ $1/2 × 1/2 ×1/2 = (100"%")/8$ = 12.5 %

Method 2

$A = \frac{A_{0}}{2^{n}} = \frac{100 %}{2^{3.0}}$ $A=A_0/2^n = (100 %)/2^3.0$ = 12.5 %